On non-rational fibers of del Pezzo fibrations over curves

2018/11/11 by Loginov, Konstantin
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.04418

Abstract

We consider threefold del Pezzo fibrations over a curve germ whose central fiber is non-rational. Under the additional assumption that the singularities of the total space are at worst ordinary double points, we apply a suitable base change and show that there is a 1-to-1 correpspondence between such fibrations and certain non-singular del Pezzo fibrations equipped with a cyclic group action.

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• Nonrational del Pezzo fibrations
• Relative linear extensions of sextic del Pezzo fibrations
• Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
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• Birational maps of del Pezzo fibrations